INSTITUTE OF PHYSICS PUBLISHING
SEMICONDUCTOR SCIENCE AND TECHNOLOGY
doi:10.1088/0268-1242/20/8/046
Semicond. Sci. Technol. 20 (2005) 886–893
Below bandgap optical absorption in
tellurium-doped GaSb
A Chandola, R Pino and P S Dutta
Department of Electrical, Computer and Systems Engineering,
Rensselaer Polytechnic Institute, Troy, NY 12180, USA
E-mail: [email protected]
Received 9 May 2005, in final form 14 June 2005
Published 18 July 2005
Online at stacks.iop.org/SST/20/886
Abstract
Enhancement in below bandgap room temperature infrared
transmission has been observed in tellurium (Te)-doped GaSb
bulk crystals. The effect of Te concentration on the transmission
characteristics of GaSb has been experimentally and theoretically
analysed. Undoped GaSb is known to exhibit p-type conductivity
with residual hole concentration of the order of (1–2) × 1017 cm−3
at room temperature due to the formation of native defects. For such
samples, inter-valence band absorption has been found to be the dominant
absorption mechanism. The residual holes could be compensated by
n-type dopants such as Te. With increasing Te concentration, free carrier
absorption due to electrons and inter-valley transitions in the conduction
subband become significant. The dependences of various absorption
mechanisms as a function of wavelength have been discussed in this
paper.
1. Introduction
Gallium antimonide (GaSb) is a technologically important
III–V semiconductor substrate material because its lattice
parameter matches solid solutions of various ternary and
quaternary III–V compounds whose bandgaps cover a wide
spectral range from 0.3 to 1.58 eV (0.8–4.3 µm) [1, 2].
GaSb-based device structures have shown potential for
applications in laser diodes with low threshold voltage [3, 4],
photodetectors with high quantum efficiency [5, 6], highfrequency devices [7, 8], superlattices with tailored optical
and transport characteristics [9], booster cells in tandem solar
cell arrangements for improved efficiency of photovoltaic
cells [10] and high-efficiency thermophotovoltaic (TPV) cells
[11]. Also, detection of longer wavelengths, 8 to 14 µm, is
possible with inter-subband absorption in antimonide-based
superlattices [12].
One of the main limitations with the antimonide
technology is the unavailability of semi-insulating (high
resistivity) or optically transparent GaSb substrates
demonstrating low absorption coefficients. Commercially
available substrates show high infrared absorption (α ≈
100 cm−1) in the below bandgap regime. It is desirable to
have the absorption coefficient as low as possible. As-grown
0268-1242/05/080886+08$30.00
undoped GaSb is always p-type in nature irrespective of
growth technique and conditions. These residual acceptors are
the limiting factors for both fundamental studies and device
applications [1]. The residual acceptors with concentration of
1017 cm−3 have been found to be related to gallium vacancies
(VGa ) and to gallium antisites (GaSb ) with a doubly ionizable
nature [13]. Efforts to reduce these native acceptors such
as growth at low temperatures (from solutions and vapour
phase) as well as from non-stoichiometric melts had limited
success [1]. Specific efforts that led to improvement in the
optical transparency in the crystals include lithium diffusion in
undoped p-GaSb by Hrostrowski and Fuller [14] and tellurium
compensation by Milvidskaya et al [15]. The latter study
only reported resistivity and transmission of GaSb at 77 K.
To the best of our knowledge, a thorough systematic study of
the optical properties of Te-doped GaSb at room temperature
has not been reported in the literature. We have been able
to enhance the transmission (reduce absorption) by impurity
compensation. This paper focuses on the analysis of the optical
absorption mechanisms in GaSb with the goal of identifying
carrier concentration that could lead to high transparency
substrates.
© 2005 IOP Publishing Ltd Printed in the UK
886
Below bandgap optical absorption in tellurium-doped GaSb
Table 1. Electrical characteristics obtained from Hall measurements
at 300 K for different wafers.
Sample
name
Type
Concentration
(cm−3)
Mobility
(cm2 V−1 s−1)
W0
W1
W6
W7
W10
W11
W12
W16
p
p
p
n
n
n
n
n
5.3 × 1016
3.2 × 1016
1.4 × 1016
2.3 × 1016
8.9 × 1016
1.3 × 1017
2.2 × 1017
1.3 × 1018
782
442
72
783
1355
3548
2592
1282
2. Experimental observations
The GaSb bulk crystal (50 mm diameter) was grown using
the vertical Bridgman technique [16]. Considering the fact
that undoped GaSb has (1–2) × 1017 cm−3 acceptors and the
segregation coefficient of Te in GaSb to be 0.37 [17], the initial
Te concentration in the melt was set at 1 × 1018 cm−3 in order
to obtain the highest level of compensation at approximately
midway along the growth axis of the boule. After growth, the
crystal was sliced into wafers and polished on both sides using
commercial alumina-based slurries [16]. W0 is the wafer sliced
from the first to freeze section of the boule with the lowest Te
concentration. The samples indices (W1 , W2 , W3 , etc) denote
the position of the wafer sliced along the growth axis starting
from W0 . The optical and electrical characterizations were
performed using a NEXUS 670 Fourier transform infrared
(FTIR) spectrometer (from Thermo Nicolet) and an EGK
HEM-2000 Hall measurement system, respectively, at 300 K.
Table 1 gives the nomenclature and electrical characteristics
of the samples [16]. In this paper, we will discuss only the
optical characteristics of the samples while correlating them
with the electrical properties (presented in table 1).
Assuming multiple reflections inside the sample (as
αt < 1 for our measured samples) and the absence of fringes,
transmission spectra can be converted to absorption spectra by
applying the following relation,
(1 − R)2 e−αt
,
(1)
1 − R 2 e−2αt
where α is the absorption coefficient and t is the thickness of
the sample. Reflectivity, R, is calculated with the assumption
that the refractive index, n, remains constant for the entire
wavelength range under consideration i.e. λ < 20 µm. Under
this assumption, R, for a normally incident beam, is given by
n−1 2
R=
(2)
n+1
T =
where for GaSb, the refractive index is taken as 3.8 [18]. With
these formulations α can be calculated at all wavelengths from
the experimentally obtained transmission spectra of the various
samples.
3. Optical absorption analyses
Very limited studies have been reported on the infrared
absorption in GaSb [19–22] compared to other III–V and
elemental semiconductors. Optical absorption mechanisms
in semiconductors have been discussed by Pankove [23].
Depending on the material, temperature and the wavelength
range of interest, various absorption mechanisms dominate
to different degrees. The optical absorption mechanisms of
interest for below bandgap absorption at room temperature are
as follows:
(1)
(2)
(3)
(4)
free carrier absorption (FCA) by free electrons;
free carrier absorption by free holes;
inter-valence band absorption by holes;
inter-valley conduction band absorption by electrons.
Depending on the relative concentration of the electrons and
holes, one or more mechanisms can be effective for a given
doping concentration in the sample.
3.1. Free carrier absorption
Scattering of free carriers leads to the absorption of the
incident radiation. Free carrier absorption by free electrons has
classically been modelled by the Drude-Zener theory which
yields
αFCA =
e3
2
4π c3 m20 0
1
n(m∗ /m0 )2
λ2
µ
N = sλ2 N
(3)
where αFCA is the free carrier absorption coefficient, n is
the refractive index, m∗ is the effective mass of the carrier,
µ is the mobility, N is the carrier concentration and λ is
the incident wavelength. However, application of quantum
mechanical principles yields different values for the exponent
of the wavelength. The exponents depend on the dominant
scattering mechanism. The collision with the semiconductor
lattice results in scattering by acoustic phonons which leads to
an absorption increase as λ1.5 [24]. Scattering due to optical
phonons gives a dependence of λ2.5 [25], while scattering by
ionized impurities gives a dependence of λ3 or λ3.5 , depending
on the approximations used in the theory [26]. According
to [23], in general all three modes of scattering are present.
Thus the overall absorption coefficient for electrons due to free
carrier absorption is given by a weighted sum of the different
processes
αFCA = s(Aλ1.5 + Bλ2.5 + Cλ3 )
(4)
where s is a constant as defined in equation (3). A, B and C
are the fitting parameters.
To reduce the number of fitting parameters, one can fit the
free carrier absorption data to the following equation,
αFCA = KFCA λm ,
(5)
where KFCA is a proportionality constant dependent on doping.
This constant also takes into account any dependence of
mobility on doping (compare equations (3) and (5)). With
this approach we will have only two parameters, namely m
and KFCA , which are easier to deduce than deriving three
independent parameters.
A similar formulation can be made to represent the free
carrier absorption due to holes.
887
A Chandola et al
3.2. Inter-valence band absorption
3.3. Inter-valley conduction band electron absorption
Valence band structure in III–V compounds is explained by
the traditional Kane model [27]. The three bands constituting
the valence band are called the heavy hole (hh), the light hole
(lh) and the split-off (so) bands. Transitions of carriers within
these bands are allowed and this gives rise to the inter-valence
band absorption.
Kahn has treated these transitions for a three band Kane
model [28]. Absorption coefficients resulting from transitions
between different bands in the valence band are given by
1
αlh−hh =
4π
√
∗5/2
16π 2 2e2h̄3/2 A2VB1 m∗hh mlh Nν 1/2
×
nc[1 + (mlh /mhh )3/2 ]m20 (m∗hh − m∗lh )5/2 (kT )3/2
hν
hν
m∗lh
m∗hh
× exp −
−
exp
−
,
kT m∗hh − m∗lh
kT m∗hh − m∗lh
(ν > 0)
(6)
Indirect electron transitions between minima at different k
of the same conduction subband have been demonstrated in
many III–V compound semiconductors. Spitzer and Whelan
point out that for wavelengths near the intrinsic band edge,
this absorption is proportional to the carrier concentration
in n-GaAs [30]. Similar transitions have been observed in
n-GaSb [31] and n-InP [32]. Lorenz et al [32] give the
following expression for the dependence of this absorption
on wavelength,
1
4π
√
∗5/2
16π 2 2e2h̄3/2 A2VB2 m∗hh mso N(ν − ν0 )3/2
×
2
∗
nc[1 + (mlh /mhh )3/2 ]m0 (mhh − m∗so )5/2 ν(kT )3/2
h(ν − ν0 )
m∗so
× exp −
, (ν > ν0 )
kT
m∗hh − m∗so
αso−hh =
(7)
1
4π
√
∗5/2
16π 2 2e2h̄3/2 A2VB3 (mlh /mhh )3/2 m∗lh mso N(ν0 − ν)3/2
×
nc[1 + (mlh /mhh )3/2 ]m20 (m∗so − m∗lh )5/2 ν(kT )3/2
h(ν0 − ν)
m∗so
× exp −
(8)
, (ν < ν0 )
kT
m∗so − m∗lh
where ν is the frequency of incident radiation, n is the
refractive index, is the permittivity, m∗lh , m∗hh and m∗so are
the effective masses of light holes, heavy holes and split-off
holes respectively, m0 is the electron rest mass and AVBi is a
dimensionless parameter. The A2VBi h̄2 k 2 is the square of the
matrix element averaged over all directions for the different
bands. AVBi is treated as a fitting parameter. Also, there has
been a large discrepancy in the reported values of effective
masses of holes in III–V compounds ([29] and references
therein). This is due to the complexity in the valence band
structures. In the light of this discussion, we treat effective
masses in the expression for inter-valence band absorption as
fitting parameters. The parameter ν0 is related to the energy of
split-off band at k = 0 and can be expressed as Eso = hν0 . For
GaSb, Eso is ascertained to be 0.8 eV [18]. Since the bandgap
of GaSb is only 0.73 eV, direct transitions from split-off band to
heavy hole band are not possible for below bandgap radiation.
So αso−hh is not considered for below bandgap absorption.
Another effect of Eso being larger than the incident radiation
is that the term (ν0 − ν) ν in αso−lh . Comparing the
terms exp(−(ν0 − ν)) to exp(−ν), we can easily determine
that αlh−hh αso−lh . Thus the inter-valence band absorption
is mainly due to the transitions from the light hole to heavy
hole band in GaSb. Hence, for the below bandgap regime the
absorption coefficient for inter-valence band absorption, αIVB ,
can be approximated by αlh−hh .
αso−lh =
888
α ∝ (h̄ω − E0 )1/2 ,
(9)
where E0 is the threshold energy for such transitions to occur.
The expression for E0 is given by [23]
E0 = E + Ep − ξn
(10)
which includes E, the energy separation between the valleys,
Ep , the phonon energy involved in the transition and ξn , the
position of the Fermi level.
Rewriting equation (9) in terms of wavelengths, we can
express the absorption due to transitions to different valleys in
the same conduction subband as
1/2
1.24
αCB = KCBV
− E0
(11)
λ
where λ is the incident wavelength, and KCBV and E0 are the
fitting parameters and they depend on the carrier concentration.
This absorption is only possible if the energy separation
between the valleys in the conduction band is comparable
to the incident radiation. This absorption coefficient decreases
with the increase in wavelength [32].
3.4. Below bandgap optical absorption coefficient
Thus the overall absorption coefficient can now be given by
α = αFCAe + αFCAh + αIVB + αCB .
(12)
We see that for a p-type sample, where p ni (where ni
is the intrinsic carrier concentration), the major contribution
to absorption comes from the inter-valence band and free hole
absorption. For an intrinsic or near intrinsic sample, both the
electron and hole contributions play an important role. For
an n-type sample, where n ni , major contribution comes
from inter-valley conduction band and free electron absorption
mechanisms. Thus depending on the carrier concentration,
the below bandgap optical absorption characteristics in GaSb
change considerably.
4. Results and discussion
Figures 1 and 2 show the transmission and absorption spectra
of p-type and n-type GaSb samples, respectively doped
with various degrees of tellurium. The transmission spectra
for p-type samples exhibit an interesting shape as shown
in figure 1. At the intrinsic band edge the transmission
attains a maximum and starts decreasing rapidly for increasing
wavelengths. However, this decrease in transmission saturates
after a given wavelength and the transmission remains
constant for higher wavelengths. The magnitude of this final
saturated transmission value seems to vary with Te doping
concentration. For the n-type samples, the transmission
Below bandgap optical absorption in tellurium-doped GaSb
(a )
(b)
Wavelength (µm)
Wavelength (µm)
Figure 1. (a) FTIR transmission spectra and (b) calculated absorption spectra for the heavily compensated p-type Te-doped GaSb samples,
namely W0 (t = 0.52 mm), W1 (t = 0.52 mm) and W6 (t = 0.58 mm).
(b)
(a )
Wavelength (µm)
Wavelength (µm)
Figure 2. (a) FTIR transmission spectra and (a) calculated absorption spectra for the n-type Te-doped GaSb samples, namely
W7 (t = 0.46 mm), W10 (t = 0.43 mm), W11 (t = 0.37 mm), W12 (t = 0.34 mm) and W16 (t = 0.33 mm).
spectra (figure 2) shows a different shape. At the intrinsic
band edge the transmission rises up to a maximum. For
lowly doped samples it is seen that the transmission remains
constant till it reaches a wavelength after which a rapid
decrease in transmission is observed. Unlike the p-type
samples this decrease does not saturate at longer wavelengths.
The characteristic wavelength after which the transmission
drops rapidly appears to be a function of extrinsic doping.
For sample W10 this characteristic wavelength seems to be
≈6.5 µm while for sample W16 which is heavily Te doped the
characteristic wavelength seems to coincide with the intrinsic
band edge. Hence, in principle one could achieve a very broad
transmission range in GaSb by fine tuning the compensation
ratio. Theoretically highest transmission possible for below
bandgap regime in GaSb is ≈49%, which is obtained by
substituting α = 0 in equation (1).
As discussed in section 3, the theoretical analysis of
the experimental transmission involves a number of fitting
parameters. However depending on the relative concentration
of electrons and holes, only a few of these parameters play
an effective role. For example, for a p-type sample such as
W0 , the effective parameters are those which are related to
the absorption due to holes, namely AVB1 , m∗lh , m∗hh and the
free hole absorption parameters (equations (6) and (4)). Other
parameters that describe the absorption due to electrons are
Table 2. Fitting parameters for inter-valence band absorption for
various p-type samples.
Fitting parameters for
inter-valence band absorption
Sample
name
Concentration
(cm−3)
m∗lh
m∗hh
AVB1
W0
W1
W6
5.3 × 10
3.2 × 1016
1.4 × 1016
0.05
0.05
0.05
0.33
0.33
0.33
33.69
31.61
32.55
16
not important for this sample. This is because the number
of electrons is so low, that physically their contribution to
optical absorption is negligible. Similarly for the n-type
samples, since the hole concentrations are so low, the effective
parameters are KFCA and m (equation (5)) for free electron
absorption and KCBV and E0 (equation (11)) for the intervalley conduction band absorption. Tables 2 and 3 present
these fitting parameters for our samples.
For the p-type samples, contribution to the absorption
coefficient arises from inter-valence band absorption (IVB)
and hole free carrier absorption (FCAh ). Since FCAh
is expected to contribute significantly only for the longer
wavelengths, on account of the λm dependence, the dominant
absorption mechanism for shorter wavelengths near the band
889
A Chandola et al
(b)
(a )
Wavelength (µm)
Wavelength (µm)
Figure 3. Contribution of inter-valence band (IVB) absorption ( ) and the hole free carrier absorption (FCA) () to the total optical
absorption (solid line) for wafers W1 and W6 (p-type GaSb). Note that the free hole absorption is negligible when compared to the IVB
contribution. Similar curves are obtained for other p-type wafers too.
(a )
(b)
Wavelength (µm)
Wavelength (µm)
Figure 4. Theoretically fitted curves (•) to experimental data (solid line) for wafers W1 and W6 .
Table 3. Fitting parameters for electron free carrier absorption and inter-valley conduction band absorption mechanisms in n-type samples
(constants valid for units of wavelengths in µm and energies in eV).
Free carrier absorption
parameters
Sample
name
Concentration
(cm−3)
Mobility
(cm2 V−1 s−1)
KFCA
m
KCBV
E0
W16
W12
W11
W10
W7
1.3 × 10
2.2 × 1017
1.3 × 1017
8.9 × 1016
2.3 × 1016
1282
2592
3548
1355
783
3.190
0.302
0.203
0.013
0.635
1.87
2.13
2.11
2.62
1.19
43.95
16.12
17.15
4.83
12.38
0.240
0.167
0.108
0.090
0.085
18
edge is expected to be IVB. Hence, the wavelength range
between 2.5 µm and 5 µm is chosen to fit experimental data
to theory for the IVB mechanism and the fitting parameters
for IVB are derived. The fitting parameters so obtained are
tabulated in table 2. Excellent fits could be obtained for
all the samples with the values shown in the table. The
absorption curve was then extrapolated for longer wavelengths
using these values to determine the contribution of the IVB
mechanism. This was then subtracted from the total absorption
curve to obtain the FCAh contribution. Contributions to hole
absorption from these two mechanisms, for wafers W1 and W6
are shown in figure 3. The figure shows absorption spectra
typical of a p-type wafer. Note that for these samples, hole
free carrier absorption is negligible. Similarly for all the other
samples, contribution from hole FCA was less than 9% of the
890
Inter-valley conduction band
absorption parameters
C
−3.0
−1.3
−0.2
0.0
−1.3
total absorption coefficient. Due to this small contribution
of FCAh , any fitting parameter is bound to have large errors
associated with it. Hence, in our analysis we choose to neglect
the effects of hole free carrier absorption. Figure 4 shows the
theoretically fitted transmission plots overlaid on experimental
data for wafers W1 and W6 . Note the excellent fit of theory
to experimental data. W1 and W6 differ only in the magnitude
of the hole concentration. Lesser hole concentration in W6
is due to increased Te content, which compensates the native
defects. It is clear that with increasing Te content, residual
hole concentration decreases resulting in enhancement in the
transmission.
For the n-type Te-doped GaSb samples the dominant
absorption mechanisms are inter-valley conduction band
(CBV) absorption and the electron free carrier absorption
Below bandgap optical absorption in tellurium-doped GaSb
(b)
(a )
Figure 5. Typical steps for theoretical fitting to experimental data for n-type GaSb sample (wafer W10 ). (a) Fitting FCA equation ( ) for
longer wavelengths where CBV absorption does not occur to the total experimental absorption spectra (solid line), (b) CBV absorption
(solid line) is obtained by subtracting extrapolated FCA contribution from the experimental absorption spectrum. This is fitted to the
inter-valley conduction band absorption equation (•).
(b)
(a )
Wavelength (µm)
Wavelength (µm)
Figure 6. For wafer W10 (a) contribution from different absorption mechanisms, CBV (•), FCA ( ) and their sum () is shown along with
experimental data (solid line). (b) Transmission curves from the fitted parameters () plotted with experimental transmission spectrum
(solid line).
(FCAe ).
Equation (5) indicates that contribution from
FCAe increases with increasing wavelengths while CBV
absorption, as given by equation (11), decreases with
increasing wavelength. For wavelengths beyond λ0 = 1.24/E0
(λ0 in µm and E0 in eV from equation (11)), this mechanism
does not contribute anymore. The closest valley above the
valley in GaSb is the L valley and the energy difference
between them is 0.08 eV [18]. The corresponding wavelength
of the radiation with this energy is 15.5 µm. Thus we can safely
conclude that CBV absorption mechanism does not contribute
beyond 15.5 µm and the sole contributor to absorption would
be the FCAe mechanism. We derive the FCAe parameters,
namely KFCA and m, by fitting equation (5) to the experimental
data between 15.5 and 20 µm. These parameters for different
wafers are given in table 3. Figure 5(a) shows the extraction of
FCAe parameters from a log–log plot for absorption coefficient
against wavelength. The contribution of FCAe mechanism
is then extrapolated for shorter wavelengths and subtracted
from the total experimental absorption spectrum to obtain
the contribution due to the CB absorption mechanism. This
remainder is then fitted to equation (11) to derive the CB fitting
parameters, namely KCBV and E0 . This step is represented in
figure 5(b). Equation (11) is modified to
1.24
− E0 + C.
(13)
αCB = KCBV
λ
The constant, C, is added to the equation to take into account
any contribution of FCAe to αCBV . Since we extrapolate
the contribution of FCAe for shorter wavelengths, there is
always either overestimation or underestimation involved in
the procedure. This might affect the fitting for CBV absorption
mechanism. The constant is a result of such extrapolation
errors. These parameters are also tabulated in table 3.
Figure 6(a) shows the contribution from the two absorption
mechanisms. Note that as expected, the contribution of FCAe
increases with wavelength while CBV absorption decreases
with wavelength. These opposite trends lead to the observed
constant transmission for wavelengths closer to the band
edge. The figure also shows the total absorption mechanism
calculated from the equations using the fitting parameters
derived in table 3. An excellent fit with the experimentally
obtained absorption spectrum is observed. The theoretically
fitted absorption spectrum is converted to the transmission
spectrum and is shown in figure 6(b) along with the actual
experimental transmission spectrum.
As the electron concentration increases from 4.2 ×
1016 cm−3 to 1.3 × 1018 cm−3, the value for E0 keeps increasing
from 0.09 eV to 0.3 eV (refer to table 3). Interestingly,
0.3 eV is the separation between the and X valleys [18].
This suggests that with increasing electron concentration,
transitions are possible between and X as well as and
891
A Chandola et al
L valleys. Additionally, the increase in carrier concentration
increases the contribution of FCAe mechanism towards the
total absorption coefficient. This contribution is strong enough
so as to mask out any effects of transitions from the to
L valley which might result in a higher value for the fitting
parameter E0 .
The exponent of the wavelength variation in the FCAe
mechanism is related to the dominant scattering mechanism as
explained in the section on theory of free carrier absorption.
The exponents for various samples are listed in table 3.
The proportionality constant, KFCA , is dependent in a
complex manner upon doping (compare equations (3) and
(5)). This is because electron mobility variation with impurity
concentration for n-GaSb is very different from other III–V
compounds. As seen in table 3, the mobility increases with
increasing Te content and then decreases again for very high
concentrations. This is accounted by the additional screening
of the electrons as the higher lying conduction band valley
gets filled up. However, after a certain concentration, electron–
electron scattering comes into effect and as a result the mobility
reduces [33]. Thus it should be noted that the variation of KFCA
is not a simple dependence on doping. However, it seems to
follow the same trend as the mobility variation with doping
(refer to table 3). This makes the optical capture cross-section
in n-GaSb, a function of doping for longer wavelengths.
From the theory presented above, it is clear that electron
concentration plays an important role in determining the
transmission characteristics. As the electron concentration
increases, theory predicts an increase in the optical absorption
(samples W10 through W16 ). Additionally, mobility also
plays an important role in free carrier absorption. With
increasing impurity concentration (samples W7 through W10 )
the electron mobility increases resulting in a decrease in
the optical absorption although the electron concentration
increases. From this discussion it can be deduced that due
to the inverse dependence of optical absorption on electron
concentration and mobility (refer to equation (3)) and the
peculiar dependence of mobility on electron concentration,
the optical absorption decreases as the impurity concentration
is increased from low to moderate values and then increases
as the impurity concentration is increased further. Thus it can
be said that for a particular impurity concentration, the tradeoff between electron concentration and mobility will be such
that the optical transmission will reach a maximum. From
table 3, for GaSb grown from stoichiometric melts, the Te
impurity concentration required for maximum transmission is
such that will give rise to an electron concentration between
5 × 1016 cm−3 and 1 × 1017 cm−3. Another way to enhance the
transmission is to reduce the number of compensating native
defect centres. A simple way of reducing the native defect
concentration is to grow n-GaSb from non-stoichiometric
melts. If the native defect concentration is reduced then
for the same Te concentration enhanced electron mobilities
are observed [33]. This provides us with low electron
concentrations as well as high mobilities, which is required
to further enhance transmission.
5. Conclusions
In conclusion, we presented the results of below bandgap
absorption studies in heavily compensated p-type and n-type
892
GaSb as a function of Te doping. For the p-type samples the
transmission starts decreasing rapidly for wavelengths below
the band edge and then saturates for longer wavelengths at a
certain transmission value. As the Te doping level increases,
the residual hole concentration reduces and an enhancement
in transmission is observed. The optical absorption in p-type
samples has been found to be dominated by the inter-valence
band absorption mechanism. For the n-type samples, the
transmission is constant for a certain range of wavelengths
below the band edge, after which the transmission starts
decreasing rapidly. The constant wavelength range reduces as
the Te concentration increases. The magnitude of transmission
increases with increasing electron concentration till n ≈
8 × 1016 cm−3, beyond which the maximum transmission
value starts decreasing for increasing electron concentrations.
These observations have been explained by taking into account
free electron absorption and inter-conduction band valley
absorption mechanisms along with the peculiar mobility
dependence on doping concentration in GaSb.
Acknowledgment
This work was supported by the National Science Foundation
(NSF) Faculty Early Career Development Award ECS
0093706.
References
[1] Dutta P S, Bhat H L and Kumar V 1997 J. Appl. Phys. 81 5821
[2] Milnes A G and Polyakov A Y 1993 Solid-State Electron.
36 803
[3] Motosugi G and Kagawa T 1980 Japan. J. Appl. Phys. 19 2303
[4] Morosini M B Z, Herrera-Perez J L, Loural M S S,
Von Zuben A A G, da Silveira A C F and Patel N B 1993
IEEE J. Quantum Electron. 29 2103
[5] Hildebrand O, Kuebart W, Benz K W and Pilkuhn M H 1981
IEEE J. Quantum Electron. 17 284
[6] Hildebrand O, Kuebart W and Pilkuhn M 1980 Appl. Phys.
Lett. 37 801
[7] Segawa K, Miki H, Otsubo M and Shirata K 1976 Electron.
Lett. 12 124
[8] Hilsum C and Rees H D 1970 Electron. Lett. 6 277
[9] Esaki L 1981 J. Cryst. Growth 52 227
[10] Frass L M, Girard G R, Avery J E, Arau B A, Sundaram V S,
Thompson A G and Gee J M 1989 J. Appl. Phys. 66 3866
[11] Williams D J and Fraas L M 1996 Proc. 2nd NREL Conference
on TPV Generation of Electricity (Colorado Springs, CO)
ed J P Benner, T J Coutts and D S Ginley (New York: AIP)
p 134
[12] Xie H, Piao J, Katz J and Wang W I 1991 J. Appl. Phys. 70
3152
[13] Baxter R D, Bate R T and Reid F J 1965 J. Phys. Chem. Solids
26 41
[14] Hrostowski H J and Fuller C S 1958 J. Phys. Chem. Solids
4 155
[15] Milvidskaya A G, Polyakov A Y, Kolchina G P, Milnes A G,
Govorkov A V, Smirkov N B and Tunitskaya I V 1994
Mater. Sci. Eng. B 22 279
[16] Pino R, Ko Y and Dutta P S 2004 J. Appl. Phys. 96 1064
[17] Dutta P S and Ostrogorsky A G 1999 J. Cryst. Growth 197 749
[18] Levinshtein M, Rumyantsev S and Shur M 1999 Handbook
Series on Semiconductor Parameters vol 2 (Singapore:
World Scientific) p 90
[19] Blunt R F, Hoseler W R and Frederikse H P R 1954 Phys. Rev.
96 576
[20] Kaiser R and Fan H Y 1965 Phys. Rev. A 138 156
Below bandgap optical absorption in tellurium-doped GaSb
[21] Iluridze G N, Titkov A N and Chalkina E I 1987 Sov.
Phys.—Semicond. 21 48
[22] Lavrushin B M, Nabiev R F and Popov Yu M 1988 Sov.
Phys.—Semicond. 22 441
[23] Pankove J I 1971 Optical Processes in Semiconductors
(Engelwood Cliffs, NJ: Prentice-Hall)
[24] Fan H Y and Becker M 1951 Semiconducting Materials
(London: Butterworth)
[25] Visvanathan S 1960 Phys. Rev. 120 376
[26] Fan H Y, Spitzer W G and Collins R J 1956 Phys. Rev.
101 566
[27] Kane E O 1956 J. Phys. Chem. Solids 1 82
[28] Kahn A H 1955 Phys. Rev. 97 1647
[29] Kolodziejczak J, Zukotynski S and Stramska H 1966 Phys.
Status Solidi 14 471
[30] Spitzer W G and Whelan J 1959 Phys. Rev. 114 59
[31] Becker W M, Ramdas A M and Fan H Y 1961 J. Appl. Phys.
32 2094
[32] Lorenz M R, Reuter W, Dumke W P, Chicotka R J,
Pettit G D and Woodall J M 1968 Appl. Phys. Lett.
13 421
[33] Baxter R D, Reid F J and Beer A C 1967 Phys. Rev. 162 718
893